While pH is used to record the acidity or alkalinity of
natural waters, we use a measurement known as normality to show the concentration
of the much stronger acid and base solutions we use in the lab. Normality
is based on molarity, but also takes into account a characteristic of acids
and bases which we will call "equivalents" and will describe in the next section.

Equivalents

Although molarity can be used to measure the concentration
of acids, it is a relatively unuseful measurement for understanding neutralization
reactions. Why? Because not every acid or base can add (or remove)
the same number of hydrogen ions from solution. Let's consider two different
acids:

Reactions of hydrochloric
acid

Reactions of sulfuric
acid

HCl
H+ + Cl-

H2SO4
H+ + HSO4-

HSO4-
H+ + SO4-2

As we see in the left side of the table, one molecule of hydrochloric
acid adds one hydrogen ion to the solution. On the other hand, sulfuric
acid releases one hydrogen ion, as shown in the first equation, then ionizes
again, releasing a second hydrogen ion. So one molecule of hydrochloric
acid could neutralize one molecule of a base while one molecule of sulfuric
acid could neutralize two molecules
of a base:

HCl + NaOH
H2O + NaCl

H2SO4 +
2NaOH 2H2O + 2NaSO4

When talking about the concentration of acids or bases, we use
measurements which involve equivalents. An equivalent is the number of moles of hydrogen
ions one mole of an acid will donate or one mole of a base will accept.
For example, hydrochloric acid has an equivalent value of 1 because each molecule
of acid donates only one hydrogen ion, so one mole of hydrochloric acid will
donate one mole of hydrogen ions. Sulfuric acid, on the other hand,
has an equivalent value of 2. To give you a couple more examples, sodium
hydroxide has an equivalent value of 1 while calcium hydroxide has an equivalent
value of 2.

Let's simplify equivalents here:

For instance, you have calcium hydroxide, Ca(OH)2. You can see there are 2 oxygen ions and 2 hydrogen ions, therefore the equivalent is 2. Another instance, sulfuric acid which is listed above, H2SO4. You can see there are 2 Hydrogen ions and 4 Oxygen ions. Since you have to have equal amounts to remove the ions, this equivalent will be 2. If you had 3 Hydrogen ions and 4 Oxygen ions, the equivalent would be 3 because you had enough oxygen ions to take care of the 3 hydrogen ions. Sodium Hydroxide, NaOH, has an equivalent of 1 since there is 1 Oxygen ion and 1 Hydrogen ion. You have to be able to have one oxygen ion for every hydrogen ion you are trying to get rid of.

Normality

Normality is the most
common measurement used for showing the concentration of acids and bases.
Normality takes into account both the molarity of the solution and the equivalent
content of the acid or base, using the equation shown below:

Normality (N) = Molarity (M) × Equivalent (N/M)

If you cancelled units in the equation above, you would find
that normality is equal to the number of moles of acid or base per liter.

Let's consider a 0.5 M solution of HCl. Since we know that
one mole of HCl contains 1 equivalent acid, we can calculate normality as
follows:

Normality = (0.5 M) ×
(1 N/M)

Normality = 0.5 N

For all acids and bases with an equivalent value of 1, the normality
of the solution will be equal to the molarity of the solution.

But not every acid and base will have a normality equal to its
molarity. How about a 3 M solution of barium hydroxide? Barium
hydroxide releases two hydroxide ions per molecule of the base, so the equivalent
value is 2. As a result, we would calculate normality as follows:

Normality = (3 M) ×
(2 N/M)

Normality = 6 N

Calculating Normality From Grams

To calculate the normality of a solution you are preparing,
you need to combine the equation for calculating molarity and the equation
for calculating normality. To simplify matters, we've combined the two
equations for you:

So what would the normality of the solution be if we dissolved 6.80 grams
of calcium hydroxide in water to produce a 0.50 L solution? First, we
have to calculate the molar mass of calcium hydroxide - 74.10 g/mol.
Then we have to figure out the equivalent value of calcium hydroxide - 2.
And, finally, we can just plug numbers into the equation:

The normality of the resulting solution would be 0.37 N.

Calculating Dilutions

Once you have calculated the normality of an acid or base solution,
you can easily calculate the concentration of any dilutions of that solution.
The formula used is essentially the same as that used for any other dilution
calculation:

N1V1 = N2V2

Where:

N1 = normality of the first solution
V1 = volume of the first solution
N2 = normality of the second solution
V2 = volume of the second solution

For example, after producing the 0.5 L of a 0.37 N solution of calcium
hydroxide in the last section, how would you dilute it to form a 0.25 N solution?

(0.37 N) (0.50 L) = (0.25 N) V2

0.74 L = V2

Based on the calculations above, we know that we have to add enough
water to the 0.37 N solution so that the total volume reaches 0.74 L.
Then we would have a 0.25 N solution.

Converting from Other Units

Converting the concentration of a solution between normality and molarity
was explained in an earlier section. We can combine the equation introduced
there with the equations introduced in Lesson 4 to convert from normality
to the other types of concentration (assuming aqueous solutions.)

For example, if you had a solution of 1 N strontium hydroxide, what
is its percent concentration?